1 Chapter 6: Stability. Chapter 6. Stability. 2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e

Transcription

1 1 Chapter 6 Stability

2 2 Figure 6.1 Closed-loop poles and response: a. stable system; b. unstable system

3 3 Figure 6.2 Common cause of problems in finding closedloop poles: a. original system; b. equivalent system

4 4 Figure 6.3 Equivalent closed-loop transfer function

5 5 Table 6.1 Initial layout for Routh table

6 6 Table 6.2 Completed Routh table

7 7 Figure 6.4 a. Feedback system for Example 6.1; b. equivalent closed-loop system

8 8 Table 6.3 Completed Routh table for Example 6.1

9 9 Table 6.4 Completed Routh table for Example 6.2

10 10 Table 6.5 Determining signs in first column of a Routh table with zero as first element in a row

11 11 Table 6.6 Routh table for Example 6.3

12 12 Table 6.7 Routh table for Example 6.4

13 13 Figure 6.5 Root positions to generate even polynomials: A, B, C, or any combination

14 14 Table 6.8 Routh table for Example 6.5

15 15 Table 6.9 Summary of pole locations for Example 6.5

16 16 Figure 6.6 Feedback control system for Example 6.6

17 17 Table 6.10 Routh table for Example 6.6

18 18 Figure 6.7 Feedback control system for Example 6.7

19 19 Table 6.11 Routh table for Example 6.7

20 20 Table 6.12 Alternative Routh table for Example 6.7

21 21 Figure 6.8 Feedback control system for Example 6.8

22 22 Table 6.13 Routh table for Example 6.8

23 23 Table 6.14 Summary of pole locations for Example 6.8

24 24 Figure 6.9 Jason is an underwater, remotecontrolled vehicle that has been used to explore the wreckage of the Lusitania. The manipulator and camera comprise some of the vehicle s control systems. Courtesy of Woods Hole Oceanographic Institution.

25 25 Figure 6.10 Feedback control system for Example 6.9

26 26 Figure 6.11 The FANUC Robot M- 400 can be configured for 4- or 5-axis of motion. It is seen here moving and stacking boxes. Courtesy of Fanuc Robotics.

27 27 Table 6.15 Routh table for Example 6.9

28 28 Table 6.16 Routh table for Example 6.9 with K = 1386

29 29 Table 6.17 Routh table for Example 6.10

30 30 Table 6.18 Routh table for Example 6.11

31 31 Table 6.19 Routh table for antenna control case study

32 32 Table 6.20 Routh table for UFSS case study

33 33 Figure P6.1

34 34 Figure P6.2

35 35 Figure P6.3

36 36 Figure P6.4

37 37 Figure P6.5

38 38 Figure P6.6

39 39 Figure P6.7

40 40 Figure P6.8

41 41 Figure P6.9

42 42 Figure P6.10 Closed-loop system with pole plot

43 43 Figure P6.11 Aircraft pitch loop model

44 44 Figure P6.12 Block diagram of a chemical process-control system

45 45 Figure P6.13 a. Soft Arm used for feeding; b. simplified block diagram Courtesy of Kazuhiko Kawamura, Vanderbilt University.

46 46 Figure P6.14 Towed vehicle roll control

47 47 Figure P6.15 Cutting force control system 1997 ASME.

48 48 Japan Air Lines/ Photo Researchers. Figure P6.16 a. A magnetic levitation transportation system; b. simplified block diagram ( 1998 IEEE)

49 49 Table 6.1 Initial layout for Routh table

50 50 Table 6.2 Completed Routh table

51 51 Table 6.3 Completed Routh table for Example 6.1

52 52 Table 6.4 Completed Routh table for Example 6.2

53 53 Table 6.5 Determining signs in first column of a Routh table with zero as first element in a row

54 54 Table 6.6 Routh table for Example 6.3

55 55 Table 6.7 Routh table for Example 6.4

56 56 Table 6.8 Routh table for Example 6.5

57 57 Table 6.9 Summary of pole locations for Example 6.5

58 58 Table 6.10 Routh table for Example 6.6

59 59 Table 6.11 Routh table for Example 6.7

60 60 Table 6.12 Alternative Routh table for Example 6.7

61 61 Table 6.13 Routh table for Example 6.8

62 62 Table 6.14 Summary of pole locations for Example 6.8

63 63 Table 6.15 Routh table for Example 6.9

64 64 Table 6.16 Routh table for Example 6.9 with K = 1386

65 65 Table 6.17 Routh table for Example 6.10

66 66 Table 6.18 Routh table for Example 6.11

67 67 Table 6.19 Routh table for antenna control case study

68 68 Table 6.20 Routh table for UFSS case study